I'm using objects as particles but the objects have hair. Why is the hair is all going sideways?
The answer has two parts.  First was that I had used a (hilariously) small amount of Gravity for growing the hair for just a touch of realism.  It is truncated in the UI to three decimal places.

Secondly, when I rotated and applied the rotation, my object was ready to be used as a particle, but it was on its side in scene space, and the hair system on the object still respected gravity in scene space.  In other words, the hair now understood gravity to be something that pulled to the side, in a sense.
But afterwards you can freely rotate an object, and as long as you don't apply the rotation the change won't be reflected in instanced objects.
So I simply rotated my reference object back 90 degrees on the X axis such that it was reaching for the sun like a good wheaty, and everything is fine. 

Reintroducing phase randomization.